g(x)=log(x+7)-log(x-5)

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Solution for g(x)=log(x+7)-log(x-5) equation: 


Simplifying
g(x) = log(x + 7) + -1log(x + -5)

Multiply g * x
gx = log(x + 7) + -1log(x + -5)

Reorder the terms:
gx = glo(7 + x) + -1log(x + -5)
gx = (7 * glo + x * glo) + -1log(x + -5)
gx = (7glo + glox) + -1log(x + -5)

Reorder the terms:
gx = 7glo + glox + -1glo(-5 + x)
gx = 7glo + glox + (-5 * -1glo + x * -1glo)
gx = 7glo + glox + (5glo + -1glox)

Reorder the terms:
gx = 7glo + 5glo + glox + -1glox

Combine like terms: 7glo + 5glo = 12glo
gx = 12glo + glox + -1glox

Combine like terms: glox + -1glox = 0
gx = 12glo + 0
gx = 12glo

Solving
gx = 12glo

Solving for variable 'g'.

Move all terms containing g to the left, all other terms to the right.

Add '-12glo' to each side of the equation.
-12glo + gx = 12glo + -12glo

Combine like terms: 12glo + -12glo = 0
-12glo + gx = 0

Factor out the Greatest Common Factor (GCF), 'g'.
g(-12lo + x) = 0


Subproblem 1
Set the factor 'g' equal to zero and attempt to solve:

Simplifying
g = 0

Solving
g = 0

Move all terms containing g to the left, all other terms to the right.

Simplifying
g = 0

Subproblem 2
Set the factor '(-12lo + x)' equal to zero and attempt to solve:

Simplifying
-12lo + x = 0

Solving
-12lo + x = 0

Move all terms containing g to the left, all other terms to the right.

Add '12lo' to each side of the equation.
-12lo + 12lo + x = 0 + 12lo

Combine like terms: -12lo + 12lo = 0
0 + x = 0 + 12lo
x = 0 + 12lo
Remove the zero:
x = 12lo

Add '-1x' to each side of the equation.
x + -1x = 12lo + -1x

Combine like terms: x + -1x = 0
0 = 12lo + -1x

Simplifying
0 = 12lo + -1x

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
g = {0}

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